A mathematical model of adaptive behavior in quadruped locomotion

Locomotion involves repetitive movements and is often executed unconsciously and automatically. In order to achieve smooth locomotion, the coordination of the rhythms of all physical parts is important. Neurophysiological studies have revealed that basic rhythms are produced in the spinal network called, the central pattern generator (CPG), where some neural oscillators interact to self-organize coordinated rhythms. We present a model of the adaptation of locomotion patterns to a variable environment, and attempt to elucidate how the dynamics of locomotion pattern generation are adjusted by the environmental changes. Recent experimental results indicate that decerebrate cats have the ability to learn new gait patterns in a changed environment. In those experiments, a decerebrate cat was set on a treadmill consisting of three moving belts. This treadmill provides a periodic perturbation to each limb through variation of the speed of each belt. When the belt for the left forelimb is quickened, the decerebrate cat initially loses interlimb coordination and stability, but gradually recovers them and finally walks with a new gait. Based on the above biological facts, we propose a CPG model whose rhythmic pattern adapts to periodic perturbation from the variable environment. First, we design the oscillator interactions to generate a desired rhythmic pattern. In our model, oscillator interactions are regarded as the forces that generate the desired motion pattern. If the desired pattern has already been realized, then the interactions are equal to zero. However, this rhythmic pattern is not reproducible when there is an environmental change. Also, if we do not adjust the rhythmic dynamics, the oscillator interactions will not be zero. Therefore, in our adaptation rule, we adjust the memorized rhythmic pattern so as to minimize the oscillator interactions. This rule can describe the adaptive behavior of decerebrate cats well. Finally, we propose a mathematical framework of an adaptation in rhythmic motion. Our framework consists of three types of dynamics: environmental, rhythmic motion, and adaptation dynamics. We conclude that the time scale of adaptation dynamics should be much larger than that of rhythmic motion dynamics, and the repetition of rhythmic motions in a stable environment is important for the convergence of adaptation. Received: 10 July 1997 / Accepted in revised form: 13 March 1998     

Application of the mathematics of coupled oscillator systems to the analysis of the neural control of locomotion.

In many animals, the activities of limb motor neurons are rhythmic during locomotion. In some animals it is known that each limb is innervated by a local control center that resides in a discrete portion of the central nervous system. Each local control center is a biological oscillator. Since each limb moves with the same frequency as each other limb and with regulated phase delay with respect to each other limb, then it follows that the local control centers are coupled to one another. The locomotory pattern generator within the central nervous system is therefore a coupled oscillator system. The mathematics of coupled oscillator systems can assist in the construction of a model of the neural pattern generator. This model can be utilized to formulate testable predictions concerning the neural control of locomotion. Experimental data gathered from organisms in several phylums are consistent with the predictions of the model.     

Constructive antagonism in limb development

Several advances have been made in our understanding of the control of the growth and patterning of embryonic limbs. Development of the vertebrate limb is dependent on reciprocal interactions between the ectoderm and mesoderm that regulate the structure and function of the apical ectodermal ridge. One key component of this regulatory program appears to be the precise control of signaling by members of the bone morphogenetic protein family via multiple antagonistic interactions.     

A walking robot called human: lessons to be learned from neural control of locomotion

From what we know at present with respect to the neural control of walking, it can be concluded that an optimal biologically inspired robot could have the following features. The limbs should include several joints in which position changes can be obtained by actuators across the joints. The control of mono- and biarticular actuators should occur at least at three levels: one at direct control of the actuators (equivalent to motoneuron level), the second at indirect control acting at a level which controls whole limb movement (flexion or extension) and the third at a still higher level controlling the interlimb coordination. The limb level circuits should be able to produce alternating flexion and extension movements in the limb by means of coupled oscillator flexor and extensor parts which are mutually inhibitory. The interlimb control level should be able to command the various limb control centers. All three control levels should have some basic feedback circuits but the most essential one is needed at the limb control level and concerns the decision to either flex or extend a given limb. The decision to activate the extensor part of the limb oscillator has to be based on feedback signalling the onset of loading of the limb involved. This should be signalled by means of load sensors in the limb. The decision to activate the flexor part of the limb oscillator has to depend on various types of feedback. The most important requirement is that flexion should only occur when the limb concerned is no longer loaded above a given threshold. The rule for the initiation of limb flexion can be made more robust by adding the requirement that position at the base of the limb ("hip") should be within a normal end of stance phase range. Hence, human locomotion is thought to use a number of principles which simplify control, just as in other species such as the cat. It is suggested that cat and human locomotion are good models to learn from when designing efficient walking robots.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Sensory Feedback Mechanism Underlying Entrainment of Central Pattern Generator to Mechanical Resonance

Rhythmic body motions observed in animal locomotion are known to be controlled by neuronal circuits called central pattern generators (CPGs). It appears that CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, the CPGs tend to induce rhythmic motion of the body at a natural frequency, i.e., the CPGs are entrained to a mechanical resonance by sensory feedback. The objective of this paper is to uncover the mechanism of entrainment resulting from the dynamic interaction of the CPG and mechanical system. We first develop multiple CPG models for the reciprocal inhibition oscillator (RIO) and examine through numerical experiments whether they can be entrained to a simple pendulum. This comparative study identifies the neuronal properties essential for the entrainment. We then analyze the simplest model that captures the essential dynamics via the method of harmonic balance. It is shown that robust entrainment results from a strong, positive-feedback coupling of a lightly damped mechanical system and the RIO consisting of neurons with the complete adaptation property     

Dispensable,Redundant, Complementary,and Cooperative Roles of Dopamine,Octopamine, and Serotonin in Drosophila melanogaster

To investigate the regulation of Drosophila melanogaster behavior by biogenic amines, we have exploited the broad requirement of the vesicular monoamine transporter (VMAT) for the vesicular storage and exocytotic release of all monoamine neurotransmitters. We used the Drosophila VMAT (dVMAT) null mutant to globally ablate exocytotic amine release and then restored DVMAT activity in either individual or multiple aminergic systems, using transgenic rescue techniques. We find that larval survival, larval locomotion, and female fertility rely predominantly on octopaminergic circuits with little apparent input from the vesicular release of serotonin or dopamine. In contrast, male courtship and fertility can be rescued by expressing DVMAT in octopaminergic or dopaminergic neurons, suggesting potentially redundant circuits. Rescue of major aspects of adult locomotion and startle behavior required octopamine, but a complementary role was observed for serotonin. Interestingly, adult circadian behavior could not be rescued by expression of DVMAT in a single subtype of aminergic neurons, but required at least two systems, suggesting the possibility of unexpected cooperative interactions. Further experiments using this model will help determine how multiple aminergic systems may contribute to the regulation of other behaviors. Our data also highlight potential differences between behaviors regulated by standard exocytotic release and those regulated by other mechanisms.     

The Expression of Locomotor Orcadian Rhythm in Female German Cockroach, Blattella Germanica (L.)

Fifteen percent of intact female German cockroaches (n = 13), Blattella germanica (L.) (Dictyoptera: Blattellidae), had weak free-running locomotor rhythmicity under 28°C and constant darkness conditions. However, 86% of ovariectomized females (n = 14) showed a strong free-running rhythm under the same conditions with a circadian period of 23.60 ± 0.15 h, similar to the male's period of 23.45±0.03 h. In addition, the locomotory activities occurred mainly during the subjective night under DD conditions as was the case in males. These results indicated that female locomotion was under the control of a circadian oscillator, which was masked by the existence of ovaries. This internal masking effect could be removed by the existence of males, but females had no effect on the locomotor pattern of another female. Since the male failed to entrain female locomotion, its role as a zeitgeber was excluded. That the locomotory pattern of the females still coincided with their reproductive cycle when exposed to male odor suggests that exposure to a male only partially removed the internal masking effects.     

Genetic interactions between clock mutations in Neurospora crassa: can they help us to understand complexity?

Recent work on circadian clocks in Neurospora has primarily focused on the frequency (frq) and white-collar (wc) loci. However, a number of other genes are known that affect either the period or temperature compensation of the rhythm. These include the period (no relationship to the period gene of Drosophila) genes and a number of genes that affect cellular metabolism. How these other loci fit into the circadian system is not known, and metabolic effects on the clock are typically not considered in single-oscillator models. Recent evidence has pointed to multiple oscillators in Neurospora, at least one of which is predicted to incorporate metabolic processes. Here, the Neurospora clock-affecting mutations will be reviewed and their genetic interactions discussed in the context of a more complex clock model involving two coupled oscillators: a FRQ/WC-based oscillator and a 'frq-less' oscillator that may involve metabolic components.     

Locomotor behavior of wild orangutans (Pongo pygmaeus wurmbii) in disturbed peat swamp forest, Sabangau, Central Kalimantan, Indonesia

This study examined the locomotor behavior of wild Bornean orangutans (P. p. wurmbii) in an area of disturbed peat swamp forest (Sabangau Catchment, Indonesia) in relation to the height in the canopy, age-sex class, behavior (feeding or traveling), and the number of supports used to bear body mass. Backward elimination log-linear modeling was employed to expose the main influences on orangutan locomotion. Our results showed that the most important distinctions with regard to locomotion were between suspensory and compressive, or, orthograde (vertical trunk) and pronograde (horizontal trunk) behavior. Whether orangutans were traveling or feeding had the most important influence on locomotion whereby compressive locomotion had a strong association with feeding, suspensory locomotion had a strong association with travel in the peripheral strata using multiple supports, whereas vertical climb/descent and oscillation showed a strong association with travel on single supports in the core stratum. In contrast to theoretical predictions on positional behavior and body size, age-sex category had a limited influence on locomotion. The study revealed that torso orthograde suspension dominates orangutan locomotion, concurring with previous studies in dipterocarp forest. But, orangutans in the Sabangau exhibited substantially higher frequencies of oscillatory locomotion than observed at other sites, suggesting this behavior confers particular benefits for traversing the highly compliant arboreal environment typical of disturbed peat swamp forest. In addition, torso pronograde suspensory locomotion was observed at much lower levels than in the Sumatran species. Together these results highlight the necessity for further examination of differences between species, which control for habitat.     

Downregulation of G protein-coupled receptors

Major advances have been made in understanding mechanisms mediating downregulation of G protein-coupled receptors. Recent studies emphasize the role of multiple proteolytic mechanisms in downregulation. A specific mechanism of downregulation, mediated by endocytosis of receptors via clathrin-coated pits followed by sorting to lysosomes, has been examined in detail. Specific protein interactions that control the specificity of G-protein-coupled receptor trafficking in this pathway are beginning to be elucidated.     

Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Motility behavior of hepatocytes on extracellular matrix substrata during aggregation

Aggregation of hepatocytes in culture is an important phenomenon to control in tissue engineering applications. Aggregation generally enhances maintenance of differentiated functions but inhibits cell growth. At present there exists insufficient information for rational design of substrata that control aggregation. Indeed, the cellular mechanism(s) underlying the aggregation process is poorly understood, although cell motility is generally considered to be an essential phenomenon. In this article we provide the first study investigating the relationship between hepatocyte aggregation and motility behavior on various extracellular matrix substrata, including Matrigel, laminin, and fibronectin. We find that the extent of aggregation depends on the concentration of the extracellular matrix proteins, as well as on the type. Furthermore, we find that the extent of aggregation appears to be independent of classical single-cell locomotion. In fact, under conditions giving rise to substantial aggregation, the fraction of cells exhibiting classical locomotion is essentially negligible. Instead, aggregation appears to involve intracellular contacts accomplished via a different form of cell motility: active cell membrane extensions followed by adhesive cell-cell interactions. An implication of these findings is that aggregation may be largely governed by relative strengths of cell-cell versus cell-substratum interactions. These observations could be helpful for improved design of cell transplantation devices and cell culture substrata. (c) 1996 by John Wiley & Sons, Inc.     

Locomotor ecology of wild orangutans (Pongo pygmaeus abelii) in the Gunung Leuser Ecosystem, Sumatra, Indonesia: a multivariate analysis using log-linear modelling

The large body mass and exclusively arboreal lifestyle of Sumatran orangutans identify them as a key species in understanding the dynamic between primates and their environment. Increased knowledge of primate locomotor ecology, coupled with recent developments in the standardization of positional mode classifications (Hunt et al. [1996] Primates 37:363-387), opened the way for sophisticated multivariate statistical approaches, clarifying complex associations between multiple influences on locomotion. In this study we present a log-linear modelling approach used to identify key associations between orangutan locomotion, canopy level, support use, and contextual behavior. Log-linear modelling is particularly appropriate because it is designed for categorical data, provides a systematic method for testing alternative hypotheses regarding interactions between variables, and allows interactions to be ranked numerically in terms of relative importance. Support diameter and type were found to have the strongest associations with locomotor repertoire, suggesting that orangutans have evolved distinct locomotor modes to solve a variety of complex habitat problems. However, height in the canopy and contextual behavior do not directly influence locomotion: instead, their effect is modified by support type and support diameter, respectively. Contrary to classic predictions, age-sex category has only limited influence on orangutan support use and locomotion, perhaps reflecting the presence of arboreal pathways which individuals of all age-sex categories follow. Effects are primarily related to a tendency for adult, parous females to adopt a more cautious approach to locomotion than adult males and immature subjects.     

Sensory Neurons Arouse C. elegans Locomotion via Both Glutamate and Neuropeptide Release

C. elegans undergoes periods of behavioral quiescence during larval molts (termed lethargus) and as adults. Little is known about the circuit mechanisms that establish these quiescent states. Lethargus and adult locomotion quiescence is dramatically reduced in mutants lacking the neuropeptide receptor NPR-1. Here, we show that the aroused locomotion of npr-1 mutants results from the exaggerated activity in multiple classes of sensory neurons, including nociceptive (ASH), touch sensitive (ALM and PLM), and stretch sensing (DVA) neurons. These sensory neurons accelerate locomotion via both neuropeptide and glutamate release. The relative contribution of these sensory neurons to arousal differs between larval molts and adults. Our results suggest that a broad network of sensory neurons dictates transitions between aroused and quiescent behavioral states.     

微小RNA和长链非编码RNA介导的昼夜节律调控

非编码RNA(ncRNA)是生物体细胞内一类重要的调控分子,其介导的昼夜节律调控日益受到研究者的重视。本文主要以黑腹果蝇Drosophila melanogaster和哺乳动物的相关研究为背景,阐述了微小RNA(miRNA)和长链非编码RNA(lncRNA)对昼夜节律的调控。miRNA介导的昼夜节律调控包括:生物体内(尤其是钟神经元中)具有节律性表达的miRNA;输入系统和miRNA存在相互调控,这主要是通过光照这个授时因子起作用;miRNA可直接调控核心振荡器,还可以调控其他基因而间接影响到核心振荡器;miRNA对输出系统的调控主要集中在代谢取食节律、运动节律、睡眠节律等。昼夜节律可调控lncRNA的表达,同时lncRNA也可调控昼夜节律,且lncRNA对基因调控范围广,作用机制复杂,这些都具有广阔的研究前景。本文将有助于进一步深入研究ncRNA对昼夜节律的调控。     

Human hepatocytes: isolation, cryopreservation and applications in drug development

The recent developments in the isolation, culturing, and cryopreservation of human hepatocytes, and the application of the cells in drug development are reviewed. Recent advances include the improvement of cryopreservation procedures to allow cell attachment, thereby extending the use of the cells to assays that requires prolong culturing such as enzyme induction studies. Applications of human hepatocytes in drug development include the evaluation of metabolic stability, metabolite profiling and identification, drug-drug interaction potential, and hepatotoxic potential. The use of intact human hepatocytes, because of the complete, undisrupted metabolic pathways and cofactors, allows the development of data more relevant to humans in vivo than tissue fractions such as human liver microsomes. Incorporation of key in vivo factors with the intact hepatocytes in vitro may help predictive human in vivo drug properties. For instance, evaluation of drug metabolism and drug-drug interactions with intact human hepatocytes in 100% human serum may eliminate the need to determine in vivo intracellular concentrations for the extrapolation of in vitro data to in vivo. Co-culturing of hepatocytes and nonhepatic primary cells from other organs in the integrated discrete multiple organ co-culture (IdMOC) may allow the evaluation of multiple organ interactions in drug metabolism and drug toxicity. In conclusion, human hepatocytes represent a critical experimental model for drug development, allowing early evaluation of human drug properties to guide the design and selection of drug candidates with a high probability of clinical success.